CHRISTOPHER BUCKELS | 9
Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
Christopher Buckels University of California [email protected]
ABSTRACT
A standard interpretation of Plato’s metaphys- ics holds that sensible particulars are images of Forms. Such particulars are fairly indepen- dent, like Aristotelian substances. I argue that this is incorrect: Platonic particulars are not Form images but aggregates of Form images, which are property-instances (tropes). Timaeus 49e-50a focuses on “this-suches” (toiauta) and even goes so far as to claim that they compose other things. I argue that Form images are this- suches, which are tropes. I also examine the geometrical account, showing that the geomet- rical constituents of the elements are also Form images. Thus everything in the sensible world is composed of tropes.
Keywords : Particulars; Tropes; Plato; Timaeus; Substance; Metaphysics; Greek Philosophy
https://doi.org/10.14195/2183-4105_18_1 10 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
1. INTRODUCTION will explain and defend the second syllogism (which may be understood as laying out a con In the Timaeus, Plato offers an account sequence of the first syllogism), and the fourth of the world whereby macroscopic physical part will consider objections. As will become objects are composed of microscopic three clear in the paper, I take Timaeus’ metaphysics ‑dimensional objects, which are, in turn, of particulars to be a version of a trope theory, composed of two‑dimensional objects. Most, and so I take τὰ τοιαῦτα to be tropes, but I will if not all, properties of macroscopic objects are defend this claim in the fourth part; I will also explained by properties of microscopic objects, consider the traditional account of particulars which are in turn explained by the configu in the Timaeus whereby Form images are bod ration of two‑dimensional objects. We seem ies (i.e., physical objects) rather than tropes. to have a completely reductionist, naturalist Let me begin by giving an initial character account of the world; why, then, is it accompa ization of a Platonic trope theory. Tropes are nied by supernatural entities such as Platonic often used to avoid commitment to universals; Forms? While I will explain why Forms are the universal or Form Whiteness, for example, crucial for the account of particulars in the could be the set of all whiteness tropes. Most Timaeus, I will be focusing not on Forms, but trope theories, therefore, are nominalist theo on sensible particulars, the three‑dimensional ries. Timaeus is not, of course, a trope nomi objects we bump into on a day‑to‑day basis, nalist; his tropes coexist with transcendent as well as their constituents. I will argue that universals, Forms.1 In his terms, a trope is a Plato does not take these particulars as basic “this‑such” (τὸ τοιοῦτον) or Form image — constituents of the physical world, but that the a trope‑theoretic interpretation of Timaeus’ ultimate constituents of Timaeus’ sensible par ontology is thus not anachronistic, since he ticulars are what metaphysicians call tropes, himself introduces tropes, as I will show, albeit or property‑instances; Timaeus calls them τὰ under the name of “this‑suches” (τὰ τοιαῦτα).2 τοιαῦτα, “this‑suches.” My argument follows: When one feels hot, one does not feel heat in general but a particular heat, this‑heat: a heat 1. Each thing that comes to be is τὸ trope. Thus the heat in a given fire is not a τοιοῦτον (this‑such). repeatable entity or “immanent universal,” 2. All and only things that come to be but a particular entity, distinct from each are images of Forms. other instance of heat. This is what I mean by 3. Therefore, τὰ τοιαῦτα (this‑suches) are a trope: a particular, non‑repeatable instance images of Forms. of a property. 4. Triangles are τὰ τοιαῦτα or are con While trope theorists generally take tropes structed from τὰ τοιαῦτα. to be fundamental entities out of which uni 5. All bodies are constructed from tri versals may be constructed, Timaeus’ tropes angles. are dependent upon transcendent universals, 6. Therefore, all bodies are constructed as “Form image” implies. So a heat trope is an from τὰ τοιαῦτα (images of Forms). image of Heat, and there can be many distinct images of the same Form of Heat, each image The second part of the paper will explain coming to be and then perishing as something and defend the first syllogism, the third part becomes and then ceases to be hot. I take Forms CHRISTOPHER BUCKELS | 11
to be immutable, non‑spatiotemporal entities The context is a puzzle about the elements, that are universals insofar as they explain com which seem to be too unstable to admit of be monality in resembling things. Heat explains ing called any one thing, since they could, at the commonality in two hot things precisely any moment, change into different elements. by having an image of itself — numerically Should we say, when pointing at a bonfire, for distinct but qualitatively identical — in each example, ‘fire is this sort of thing’ rather than hot thing; i.e., two hot things resemble each ‘fire is this thing’, or should we say ‘this sort of other because each contains a heat trope. thing is fire’ instead of ‘this thing is fire’? A trope‑bundle theorist would say that However one wishes to settle this dispute, sensible particulars are wholly constituted we can focus on “this‑such” and identify two by tropes. Fire is a bundle of heat, color, etc. main interpretations of τὸ τοιοῦτον in the pas While I do not here defend a Platonic trope- sage. The first, dubbed the ‘traditional transla bundle theory, my arguments naturally lead tion’ by its adherents, claims that τὰ τοιαῦτα to such an interpretation. My trope‑theoretic are “temporary characteristics” rather than interpretation of the Timaeus differs from tra “self‑subsistent” things (Zeyl 2000 lviii, n. 18). ditional interpretations in that it takes tropes The second, which Zeyl calls the ‘alternative rather than sensible particulars as images of translation,’ takes τὰ τοιαῦτα to be “distinct Forms. Instead of holding that sensible par and self‑identical characteristics” or “recurrent, ticulars have their properties by participat stable, and determinate characters” (following ing in Forms, a trope‑theoretic interpretation Cherniss 1954). I propose, for now, to follow a holds that sensible particulars have properties middle ground, calling them “characteristics;” by having tropes as constituents. Thus Forms we will leave aside whether they are “tempo and their images — in contemporary terms, rary” or “recurrent, stable, and determinate.” transcendent universals and tropes — play We are left with quite a bit of agreement. On the central role in Plato’s explanation of the the one hand, these characteristics are tempo sensible world, rather than sensible particulars rary in at least one sense: they may be at a cer playing the starring role. tain place for only a short time, and that place may be occupied by a different characteristic at any time. Thus the fiery characteristic may 2. τὰ τοιαʋ ̃τα be replaced by a watery characteristic at any moment. On the other hand, these character 2.1. EACH THING THAT COMES TO BE IS istics are stable and determinate in at least one τὰ τοιαʋ ̃τα sense: for as long as each exists—which may be only an instant—it is that characteristic and not Timaeus introduces τὰ τοιαῦτα at 49d5, some other. It may be identified as belonging in the midst of a very controversial passage.3 to a certain kind. So the fiery characteristic is At the heart of the controversy is whether we fiery for as long as it exists, even if is replaced should take Timaeus to say, “fire is τὸ τοιοῦτον by a watery characteristic in but a moment. (“this such” or “this sort of thing”), rather than On either translation, Timaeus generalizes τοῦτο (“this” or “that”)”, or, “τὸ τοιοῦτον, not his conclusions to “everything that comes to τοῦτο, is fire.” The debate is thus over which be” (49e7). Thus every generated entity is a terms are subjects and which are predicates. characteristic, not a ‘thing;’ the characteristic 12 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
may be replaced at any time by another char that it is an image (τόνδε τὸν κόσμον εἰκόνα acteristic, but it remains what it is as long as τινὸς εἶναι, 29b1‑2), viz., an image of an eter it is. If we generalize this claim, it applies to nal, changeless model (παράδειγμα, 29a2‑b2). any characteristic, e.g., that of being a garbage So the demiurge, a divine craftsman, looks to truck, not just to elements. And there is no rea Being in order to make the universe, which is son to think it does not apply completely gen an image of the Living Being that contains all erally, since Timaeus gives “hot” and “white” the intelligible living beings as parts just as as further examples. Even if we think that the the universe contains us and all the other vis properties of being hot and being white are ible creatures (30c2‑d1). I take the “intelligible suggested from our discussion of fire, they are living beings” to be Forms of animal species, widely applicable to macroscopic objects, and e.g., the Form of Human Being, the Form of we are given no reason to restrict their use to Goat, etc. The Living Being that contains all describing elements. In fact, Timaeus cannot be the others would be, then, the Form of Living restricting his argument to elements, since he Being, i.e., the transcendent universal that ex extends it to “anything you can point to,” and plains what all living beings have in common.6 it is not, strictly speaking, possible to point to Thus we have reason to identify Being with an element, since they are microscopic particles Forms, an identification that is confirmed, (we can point to some fire or water, but these e.g., at 51d3‑52a4. The parts of the universe are macroscopic bodies composed of appropri on which Timaeus focuses, then, are the liv ate elements). Thus we should regard Timaeus’ ing parts (including heavenly bodies, which proscription as perfectly general, as he insists are created gods), and these are all images of several times: do not call anything that comes animal Forms. In fact, later in the Timaeus Be to be τοῦτο, but each thing that comes to be coming is explicitly identified with the class of is τὸ τοιοῦτον.4 Form images (48e4‑49a1), so that each thing in Becoming is an image of a Form. It is not clear, at this point, what it means to be an “image” of 2.2. ALL AND ONLY THINGS THAT a Form, but this will become clearer when we COME TO BE ARE IMAGES OF FORMS identify images of Forms with τὰ τοιαῦτα. Timaeus’ second account marks a signifi Timaeus gives two accounts of the universe’s cant change in our ontology: instead of two generation, which I take to be complementary kinds, Being and Becoming, we now have a in at least the minimal sense that the second third, the Receptacle. I will presuppose as little does not annul the first.5 We have focused on about the Receptacle as possible, since it is a the second thus far. In his first account, Ti controversial subject.7 What I will emphasize is maeus distinguishes between Being and Be that everything that comes to be — everything coming. He does not specify the members of in the class of Becoming — is an image of a Becoming — which would, it seems, include Form.8 It is controversial to say that Becoming everything in the changeable, sensible world is unchanged between the first and second ac — but he begins with an informative example: counts, as some think that the first account’s the universe, taken as a whole, is in the class of Becoming is separated into the Receptacle Becoming. In addition, he offers a character and Becoming of the second account.9 But if ization of this exemplum of Becoming, namely we bracket the Receptacle, we can apply the CHRISTOPHER BUCKELS | 13
later rule — that everything that comes to be Itself, mentioned at 51b8, would certainly be is an image of a Form — to the first account, understood best as Fieriness, not as a great fire especially since Timaeus’ first and primary in heaven. It is distinct from each particular exemplum of Becoming, the universe itself, is fire, but it explains why each particular fire is explicitly an image of a Form. Thus Form im fire; we should understand this to mean that ages are the things that come to be, and things Fieriness explains why each particular fire, that come to be are Form images. each with the characteristic of being fiery, is fiery, rather than being some other quality. There are many fiery things: each fieriness, 2.3. THEREFORE, τὰ τοιαʋ ̃τα that is, each particular characteristic of being (THIS-SUCHES) ARE IMAGES OF FORMS fiery, is a paticular image of Fieriness itself, just as each just character is a particular image of Earlier we found Timaeus extending his Justice itself. conclusions about fire to “everything that A word about the Receptacle: while Timaeus comes to be.” Thus each thing that comes to denies that anything that comes to be is a this, be is τὸ τοιοῦτον. It is not a thing — at least he turns around to argue that there is a this not as we usually conceive ‘things,’ as physi that can be stably designated, although it is cal objects with many characteristics — but a not essentially characterized, i.e., in itself it characteristic. Now we have seen that Form im has no properties, or at least no properties that ages exhaust the category of Becoming; Form correspond to Forms. The Receptacle evidently images are those things that come to be. Thus has the stability that particulars lack, so that it Form images are τὰ τοιαῦτα. This makes per can be designated reliably, even though entities fect sense, at least if we think of Forms such are constantly coming to be in it and perishing as Goodness, Justice, and Beauty. Being good, from it. So when we attempt to designate a bit of being just, and being beautiful are characteris flame with a demonstrative “this,” we actually tics, not things; they characterize things. So an designate the bit of the Receptacle in which the image of Goodness should be the characteristic bit of flame appears. When we say “that is fire,” of being good that some particular thing has. speaking normally, what we really do is pick out An image of Justice is the just character of a a location in the Receptacle and assert that it particular person or action. And the image of is fiery, i.e., that there is an image of Fieriness Beauty a beautiful painting possesses is the in that region of the Receptacle.10 characteristic of its being beautiful. A proper treatment of the Receptacle, But what about other Forms? One of the whether it is space, substratum, both, or neither, Forms explicitly discussed in the dialogue is would take us too far afield, but let us return to Fire, which Timaeus says must exist over and the traditional and alternative interpretations. above all sensible fires (51b7‑52a4). But fire is Partisans of the traditional interpretation point not, one might think, a characteristic. Fire is a out that, according to the alternative, we are thing, at least for the ancient Greeks; it is, after using our normal, everyday terms incorrectly.11 all, an element. Timaeus, however, explicitly We are wrong when we point to a bonfire and denies that fire is a thing at 49d5, telling us name it “fire,” since we should only use “fire” to that fire is τὸ τοιοῦτον (or that τὸ τοιοῦτον is name the characteristic common to it and every fire). We should think of fire as fieriness; Fire other bonfire. This accusation is, of course, 14 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
true; in fact, it seems that the main point of the The Receptacle stands on its own, but fire is passage is that we use our everyday terms in parasitic. a loose and derivative manner. Strictly speak Despite their equivalence, the traditional ing, we apply terms incorrectly. Although its translation is used to support an interpreta partisans do not appear to recognize it, the tion whereby particulars in the Timaeus are traditional translation actually presupposes a self‑subsistent substances.12 According to Zeyl, corresponding error, since we only correctly such substances endure over time as the sub name a bonfire “fire” if we are using the name jects and substrata of various characteristics adjectivally, not designating the bonfire as a such as fire.13 Such a reading relies heavily on self‑subsisting thing but only as a temporary an interpretation of the Receptacle as a sub characteristic of that space. But our everyday stratum and cannot be based simply on the use of the term “fire” is intended to pick out translation we have examined. In other words, a real, independent thing, not a property: we the traditional translation is not sufficient for think there really is a thing there, even if it is a substance‑interpretation of particulars; what a thing I can pass my hand through. For ex we have, on either translation, are character‑ ample, when I get burned by some fire, I think istics, not things, coming to be. These charac that there must be a thing there that burned teristics, or τὰ τοιαῦτα, are images of Forms, me. Since fire may be a strange example of a and they exhaust Becoming. Taking Forms to thing to our modern ears, let us instead take exhaust Being, then, we would be left with three a hunk of earth. According to the traditional ontological categories: Forms, Forms images translation, earth is a temporary characteristic (τὰ τοιαῦτα), and the Receptacle. of a part of the Receptacle, not a self‑subsisting thing. Calling a hunk of rock “earth,” then, is correct only if we are applying the name not 3. TRIANGLES to a this but to a characteristic. The alternative translation insists that the name “earth” picks We have identified all things that come to out the characteristic common to this hunk and be with images of Forms and hence with τὰ each other hunk of earth, rather than picking τοιαῦτα. But there is another account of the out the physical thing. generation of macroscopic objects in the Ti‑ The two translations, then, have equiva maeus, namely, that sensible particulars are lent conclusions: our normal terms pick out composed of more fundamental particles— temporary characteristics, not self‑subsisting what I will call elemental triangles. In this things. The difference is that the traditional section of the paper I will show that these tri interpretation allows us to speak of what we angles are τὰ τοιαῦτα or are themselves com see as fire, while qualifying the nature of fire posed of τὰ τοιαῦτα, so that our account of so that it is not the kind of thing to which we sensible particulars stands. Before we discuss think we are referring, while the alternative these triangles, though, we need to address the prohibits us from calling what we see fire, if context of the passage, where Timaeus tells us we are to speak correctly, since the nature of that the demiurge brings an unorganized uni fire is far different from what we suppose it is. verse, full of formless “vestiges” of elements in According to both translations, fire is a charac discordant motion, into a whole organized by teristic, characterizing a bit of the Receptacle. form and number. There are two readings of CHRISTOPHER BUCKELS | 15
this text, a literal, which takes the divine cre does, however, seem to be structural, since fire ation in time at face‑value, and a non‑literal, is instantiated whenever there is an instance which takes the cosmos to be eternal and, thus, of a given structure — i.e., whenever elemental reads this passage as a myth.14 At stake is the triangles are arranged in a certain way. Thus we status of the elements in the pre‑cosmic state: preserve the prior reference to fire as this‑such, did “vestiges” of elements actually exist, and i.e., such a structure as this, one that includes a thus must be accounted for, or are they simply a certain color, heat, and other properties. These relic of the mythic form of Timaeus’ discourse? properties taken by themselves, scattered across I believe my account is neutral between these the Receptacle, do not constitute a fire, but they two readings, but I owe partisans of the literal do so when they are arranged correctly, i.e., reading an explanation of how my account is when there is a structure that includes these compatible with pre‑cosmic vestiges, so I will this‑suches. return to this point after discussing the con Looking ahead, Timaeus explains fire’s sen struction of elements. sible properties by reference to properties of its Elements are, Timaeus tells us, bodies geometrical constituents; fire is hot because (σώματα, 53c4‑5). Thus, he infers, they are of the small, sharp nature of its body’s angles composed of triangles, since bodies have depth, (61d5‑62a5). Fire’s nature is not, then, qualita things with depth have planar surfaces, and tive, e.g., to be hot, since its heat is explained planes may be broken into triangles. Each ele by reference to its geometrical structure. Heat mental body of fire, for example, is a four‑sided is a necessary property of fire; it is included as pyramid with faces composed of six 30‑60‑90 a necessary consequence of fire’s structure, as triangles, and these triangles, when dissolved we see when Timaeus describes the smallness, from their current structure, may join with sharpness, and lightness of fire (55e7‑56b2). If others to form molecules of water or air. Each fire’s other qualities can be explained likewise, elemental body is defined by its number and and there is no reason to think they cannot, form, i.e., a certain number of such‑and‑such then fire is simply a structure that necessarily triangles organized into such‑and‑such a shape. includes certain properties. Thus, elements’ So wherever triangles are combined into a tet natures are their geometrical structures.15 rahedral pyramid, there is fire. These elemental The Form of Fire is structural.16 Notice that triangles come to be in the Receptacle, thereby we need not say that all tetrahedral pyramids forming parts of the geometrical figures that are fires, since fire need only be one of the in compose elemental bodies, and elemental bod finite possible kinds of tetrahedral pyramids; ies, i.e., fire, earth, air, and water, in turn, form in addition, we need not worry that a macro ordinary, sensible particulars. scopic tetrahedral pyramid might burst into Although he has not said it here, Timaeus flames, if it had the right proportions, since must be speaking of the sensible, generated fire is a structure of elemental triangles, not a elements — sensible fire, sensible water, etc. structure of just any triangles.17 It might help — because he tells us earlier that bodily things to think of the Fieriness as a universal with are sensible and thus also generated (28b7‑c2). twenty‑four slots (four faces of six triangles So we should not immediately conclude that each), each slot being filled by the Form of the the Form of Fire is composed of elemental tri appropriate triangle;18 when fire is instantiated, angles, since it is not a body. The Form of Fire the twenty‑four triangles are also instantiated, 16 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
since the fire trope relates the triangle tropes, and bodies does not lock us into a particular which, in turn, relate angle tropes, etc. interpretation of the Receptacle, since we have I can now return to the literal reading of the nowhere assumed that the triangles are bodily demiurge’s organization of the pre‑cosmic ves or material. In fact, the triangles cannot be tiges. Let us assume that the vestiges had some bodily, since bodies have depth (53c5-6) and structure, although imperfect, so that we may plane figures have no depth. It is also dif continue to assign the nature of the elements ficult to hold that they are material, since to their geometrical structures.19 Fieriness is they are, again, only two‑dimensional.20 For structural, and there are imperfect instances the same reason, it is difficult to assign any of this structure in the Receptacle even before ‘containing’ ability to the triangles, in order the demiurge sets to work. Each instance of that they may hold in ‘stuff’ that then makes fire would, in these pre‑cosmic conditions, be particulars material: a plane can offer no kind inexactly formed, perhaps with irregular con of resistance, let alone contain something.21 stituents or no constituents at all, such that it The triangles do, however, compose elemen would be prohibited from transforming into tal bodies which, in turn, compose material the other elements in the way that fire can af particulars, so there is some temptation to ter its geometrical construction. At the time call them material. “Material” will, however, of creation, the demiurge assigns a number mean something peculiar. Contemporary sci to each structure, i.e., he looks to Fieriness ence has acclimated us to the idea that the and imitates its geometrical structure in the most basic constituents of reality—funda Receptacle, crafting fiery bodies out of a cer mental particles—are very different from the tain number of elemental triangles, which are objects we see and with which we interact. in turn formed in the Receptacle. Since this Just so, Plato’s two‑dimensional triangles are structure has been imposed on the bodily ele material in a stretched sense,22 in the same ments, they now have a certain regularity and way that non‑extended simples might be said stability: each molecule of fire is a pyramid to be material in a theory that takes them as with regular faces composed of triangles, and basic constituents of material objects. these triangles, when dissolved from their cur Second, we seem to have left Form images rent structure, may join with others to form behind. How do we reconcile them with el molecules of water or air. In other words, there emental triangles? There are two main pos are now rules for an orderly transition from one sibilities: first, that triangles are composed of element to another, and each elemental body this‑suches, even though they are not bodies, is defined by its number and form. Thus my and second, that triangles are, themselves, interpretation of the elements can be reconciled simple images of Triangularity, i.e., images with either a literal or a non‑literal reading of with no further components. While the lat the dialogue’s creation story. ter suggestion would be fully compatible with My account of the elements and their con the interpretation presented above, I do not struction raises several concerns. First of all, think it correct, since elemental triangles have one might wonder about the consequences multiple properties. Timaeus recognizes this of my account for the interpretation of the when he describes his reasoning in selecting Receptacle as material or nonmaterial. But the ‘best’ triangles: triangles are right‑angled, my account thus far of elemental triangles trilateral, shaped, etc. If there is a Form for CHRISTOPHER BUCKELS | 17
each of these properties, elemental triangles Form images. Being hot is τὸ τοιοῦτον (50a2). must be composed of Form images. Since τὰ τοιαῦτα are Form images, heat is a One may object, however, that I am assum Form image. Fire is, of course, hot, and Ti ing that triangles and their properties are Form maeus explains this fact by appealing to its images, but Timaeus never explicitly calls them geometrical construction. Fire is a four‑sided such. Let us recall our treatment of fire. When pyramid with acute angles. These small, sharp we say colloquially, “this is fire” (or, “fire is angles cut flesh, and that is what we call heat this”), what we should really say, if we were (61d5‑62a5). And so heat, an image of Heat, is speaking perspicuously, is that this is a part a property of the elemental body of fire. Since (region) of the Receptacle in which has come everything made out of hot etc. are τὰ τοιαῦτα to be this‑fieriness. We can generalize this rule (50a3‑4), and τὰ τοιαῦτα are images of Forms, to other parts of the Timaeus, even though Ti pyramids must also be images of Forms. There maeus speaks in a more colloquial manner in is no reason to think that the elemental tri other places. When he speaks of triangles, it angles composing those pyramids — triangles might seem that they abide in a way that fire which are also made out of their properties — does not. But we could no more pick out “this are any different. So elemental triangles are triangle” or “this pyramid” than we could “this Form images or composed thereof, and the fire.” In the case of “this fire,” we pick out a por mechanistic explanation of heat is compatible tion of the Receptacle and a Form image, viz., with bodies being composed of Form images. an image of Fieriness. Similarly, when we say One may press the worry about triangles “this triangle,” we are speaking loosely, picking and Form images, however, and formulate a out a portion of the Receptacle and an image of ‘third wave’ or ‘greatest difficulty’ for my in Triangularity. There is no more reason to think terpretation of the elemental triangles: such tri that this‑triangle abides than to think that this- angles, it seems, abide and persist in a way that fire abides. If fire flees the use of “this,” then so τὰ τοιαῦτα do not, and thus elemental triangles should triangles. Thus, an image of Triangular are not subject to the worry about elements that ity is a this‑such on the same ontological level leads Timaeus to formulate the this/this‑such as an image of Fieriness or Heat. distinction. In fact, one might say, elemental In fact, the passage immediately following triangles are the solution to this worry: they the “much misread” passage about fire tells us, must persist to underlie the geometrical ac explicitly, that a triangle is a this‑such. At 50a5 count of elemental transformation. ‑b5, when Timaeus tells us not to call a golden My account might lead us to think, in triangle “triangle” but “gold,” he goes on to say contrast, that triangles are as unstable as any that we should be content if the triangle (or other this‑such. They could, at any moment, any other figure molded in gold) accepts the change into anything else. Indeed, we might designation of τὸ τοιοῦτον. Since the mean even be tempted to say that elemental trian ing of “triangle” has not changed between 50a gles are new at every moment, i.e., that each and 53c, we should continue to see triangles as triangle in the universe undergoes so‑called this‑suches, instances of Triangularity, which immaculate replacement, being replaced by a partially constitute elemental triangles. seemingly identical triangle each instant, so We have another reason to consider elemen that, technically, “nothing is ever the same” tal triangles as derivative objects composed of (Phaedo 78e3‑4). Although this is a tempting 18 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
way to explain Plato’s persistent calls for flux compose marrow, or both — are destroyed. in the sensible world, there are reasons to doubt This is also how we should read the claim about that elemental triangles are as unstable as the triangles’ bases, namely, that these refer to how elements they underlie. First, it is not obvious triangles are put together to form the faces of what triangles would change into unless they regular solids. When their bases weaken, tri undergo immaculate replacement, and then we angles are more likely to come apart from each are seemingly positing immaculate replace other, destroying marrow and releasing soul ment just to ensure that things are “never the from body. Triangles themselves re‑form with same,” which is circular. Second, it seems that other triangles to compose different elements, triangles must persist so that the elements can although I do not deny that triangles could, in change into each other. It is clear that the same principle, be destroyed; they are, after all, parts triangles that compose a body of fire can go on of Becoming. Timaeus also seems to refer to to compose a body of air (56e2‑7). the same triangles throughout his description Third, Timaeus’ discussion of aging (81b5 of aging, rather than immaculately replaced ‑e5) seems to require that elemental triangles duplicates.23 Thus triangles seem to persist persist. He tells us that in newly constructed for some time, since they can be “fresh” and living things, elemental triangles are “fresh” newly constructed or “older” and more weakly and “straight from the stocks” (νέα μὲν οὖν bonded together. σύστασις τοῦ παντὸς ζῴου, καινὰ τὰ τρίγωνα While it may be that some tension is un οἷον ἐκ δρυόχων ἔτι ἔχουσα τῶν γενῶν, 81b5 avoidable, as Timaeus himself admits (29c4‑7), ‑7). They are firmly locked together and so in such an ambitious account of the universe, they easily overcome and cut up the “older” we can allow some groups of τὰ τοιαῦτα to (παλαιότερα) incoming triangles from food. be more stable than others; in fact, we have But when a triangle’s “base” weakens (literally, independent reason for allowing such a pos its “root,” ἡ ῥίζα τῶν τριγώνων χαλᾷ, 81c6‑7), sibility, for the heavenly bodies have come to the living thing’s triangles can be overcome by be and yet appear to be indestructible. Timaeus entering triangles, and it enters old age. Death posits τὰ τοιαῦτα to distinguish Form images comes when the soul is released, which happens and the Receptacle, since Form images have a when the interlocking bonds of the marrow’s precarious ontological stability, due to their triangles no longer hold together (τῶν περὶ τὸν complete dependence on Forms and Receptacle, μυελὸν τριγώνων οἱ συναρμοσθέντες μηκέτι and the Receptacle is not dependent on Form ἀντέχωσιν δεσμοὶ τῷ πόνῳ διιστάμενοι, 81d5 images for its existence and stability. Even if ‑6). Marrow, which anchors soul to body, is elemental triangles or heavenly bodies have a made of specimens of the elements with the stability that other particulars lack, they are most precise triangles (73b5‑8). still composed of images, dependent upon While the information about aging and originals (e.g., Triangularity) and a medium, death might lead us to believe that elemental and so flee the designation of ‘this’ or ‘that.’ triangles are themselves destroyed, this is a They are still destructible, derivative, and im doubtful reading of the passage. Instead, it permanent. In these respects, they are no more seems that the bonds between triangles — ei entities in their own right than elements or ther those which hold triangles together into other particulars, for they are constructed of elements, or those that hold them together to more basic entities — τὰ τοιαῦτα correspond CHRISTOPHER BUCKELS | 19
ing to their properties—and these more basic their instantiations. For example, if white were entities are fully dependent upon Forms and an immanent universal, there would be only the Receptacle. one white, although it would be in many places at the same time. Whiteness would ‘recur’ ev ery time there is a white thing, but it would be 4. TROPES the same whiteness — numerically one and the same — that is ‘in’ each white thing. In Timaeus’ τὰ τοιαῦτα are, I have been con contrast, there are many white tropes, each dis tending, tropes, which metaphysicians still call tinct from the other, but each is equally white. this‑suches.24 Consider that, for any property For a trope theorist, Whiteness recurs in white Fness corresponding to predicate F, we can al things in the sense that each white thing has ways call an instance of Fness F. An instance a numerically distinct white trope ‘in’ it. So if of fieriness is always fiery—a fiery trope is Form images are immanent universals, then fiery—whenever it exists. But predicates can an image of Justice would be one and the same not be applied in a stable, permanent way to in all instances of Justice, ‘recurring’ in each any concrete subject that has come to be, since instance. But if Form images are trope‑like, any thing or stuff could be characterized by a then there are many images of Justice, each different predicate, as Timaeus shows at 49d4 one distinct and fleeting. ‑6. Predicates can only be applied to tropes and A trope‑theoretic reading can respond to then derivatively to aggregates of tropes, i.e., this difficulty by emphasizing that the Form, the things “composed of hot and white and the not the image, recurs; the same Form is imaged, opposites.” We can concisely demarcate Plato’s so a characteristic “comes around always in ontological division between Forms and Form similar fashion” because a single Form is im images as the division between properties (uni aged in many locations, not because there is versals) and instances (tropes).25 a single, multiply‑located image.27 Whiteness recurs in every instance of white because there is an image of one and the same Form in every 4.1. IMAGES OF FORMS ARE NOT instance, even though each image is numeri IMMANENT UNIVERSALS cally distinct from every other image. The trope‑theoretic reading is, in general, One may object that τὰ τοιαῦτα are not preferable to the immanent universal reading, tropes but immanent universals (or ‘immanent since Forms would be redundant if there were forms’).26 Timaeus 49e4‑7, which gives a more immanent universals. Immanent universals complete formula for τὸ τοιοῦτον (“this‑such would do all the work for a theory of universals coming around always in similar fashion in in a way that tropes do not, since, according to each case and all together”), seems to raise a a trope‑theoretic interpretation of Plato, Forms difficulty for taking Form images as tropes, still serve as unitary, eternal properties and since τὰ τοιαῦτα here seem more like imma objects of knowledge. With immanent univer nent universals; it seems that one and the same sals, however, there is already a property that ‘sort of thing’ recurs in multiple instantiations. is immutable and can serve as an object for This recurrence would fit well with immanent knowledge, so we have no need of Forms in universals, which are one and the same in all of addition. Since the Timaeus clearly makes use 20 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
of separate Forms—for instance, Timaeus ar In fact, the universe is no more an ob gues that Fieriness is distinct from sensible fires stacle to a trope‑theoretic interpretation of (51b7‑c5) — and, moreover, Forms are justified the Timaeus than is fire, since both are, in precisely because they are objects of knowledge fact, bodies. Just as fire is an elemental body (51d3‑52a4), the trope‑theoretic interpretation composed of its properties, so is the universe of τὰ τοιαῦτα is preferable.28 a body composed of its properties.29 Let us So, if we dismiss an immanent universal review fieriness; it is a structural property, interpretation of τὰ τοιαῦτα, which treats an arrangement of other properties, includ them as repeatable, multiply‑located enti ing heat—which turns out to be the acuteness ties, we are left with a trope theoretic inter of the fire molecule’s angles. Notice that the pretation, which treats each Form image as fiery trope is structural; it does not have other a distinct, non‑repeatable entity located in properties, but it structures them. Whenever one spatial region. To be clear, taking Form fire is instantiated, a certain arrangement is images to be tropes amounts to no more than also instantiated, specifically, a tetrahedral this, i.e., saying that they are non‑repeatable pyramid of elemental triangles. This seems instances of properties that are each located to an observer to be an object, i.e., a fire, and in exactly one spatial region at a time. As it is the apparent fire that we say is hot, not the long as Form images are instances of prop fiery trope. The fiery trope is not itself hot, but erties, then we have an exhaustive division always includes heat, which is hot. between interpretations that take them to Since the other elements are explained be each located at one spatial region (tropes) similarly, we should explain all substantive and those that allow them to be multiply Forms similarly. Supposing there are Forms ‑located in space (immanent universals), as of living things, since the Living Being and well as reason to prefer the trope‑theoretic ‘other intelligible animals’ play an important interpretation. role as models (παραδείγματα) in creating the universe, these Forms should be under stood as structures parallel to the elements. 4.2. IMAGES OF FORMS ARE NOT BODIES In fact, the Living Being seems simply to be a structure of animal Forms; the Form If Form images are instances of proper of any particular animal, such as Human ties, then they are tropes. But, despite my ar Being (or Humanity), would, in turn, be an gument that all Form images are τὰ τοιαῦτα arrangement of various parts that make up and τὰ τοιαῦτα are Forms images, one might human beings. These parts include physical find in Timaeus’ first account of the universe parts such as hearts, which will in turn have a counterexample to taking them as property parts, ending with elemental triangles and ‑instances. There, it seems, Timaeus discusses their constituent tropes; but human beings things, or bodies, not properties, as images of also include non‑physical parts such as vir Forms. For example, the universe is an image of tues and rationality. These latter components the intelligible Living Being. But the universe is are Form images, too, and components in the not a property; it is a thing with properties. So structure of Humanity just as are the physi can we say it is τὸ τοιοῦτον without discarding cal parts, since all are, in the final analysis, Timaeus’ first account? composed of tropes.30 CHRISTOPHER BUCKELS | 21
5. CONCLUSION BIBLIOGRAPHY
I have argued that the second category in Armstrong, D. M. 1989. Universals: An Opinionated Introduction. Westview Press. Plato’s tripartite ontology, that of Becoming, Broadie, Sarah. 2012. Nature and Divinity in Plato’s is the category of Form images. Moreover, I Timaeus. Cambridge. argued, Form images are tropes, i.e., proper Buckels, Christopher. 2016a. “Making Room for Par ty-instances, rather than bodies or immanent ticulars: Plato’s Receptacle as Space not Sub universals, and particulars are composed of stratum,” Apeiron 49:3, 303‑328. tropes. The elemental triangles introduced to … 2016b. “The Ontology of the Secret Doctrine in constitute particulars turn out to be composed Plato’s Theaetetus,” Phronesis 61:3, 243‑259. of tropes as well, so that tropes and things Campbell, Keith. 1990. Abstract Particulars. Oxford. composed of tropes exhaust the category of Cherniss, Harold. 1957. “The Relation of the Timaeus to Plato’s Later Dialogues.” The American Journal Becoming. There is, then, no place for sensible, of Philology 78: 3. 225 – 266. material particulars in Plato’s fundamental on … 1954. “A Much Misread Passage of the Timaeus tology. Instead, such particulars are deriva (Timaeus 49C7‑50B5).” The American Journal tive entities, constructed from Form images of Philology 75: 2. 113 – 130. which are, in turn, dependent on Forms and Cornford, Francis. 1937. Plato’s Cosmology: TheTi maeus of Plato. Hackett. the Receptacle. While Aristotle distinguishes Ehring, Douglas. 2011. Tropes. Oxford. between kinds (substances), such as human be Ferber, Rafael. 1997. “Why Did Plato Maintain the ings and animals, and other properties, such as ‘Theory of Ideas’ in the Timaeus?” In Tomás qualities, quantities, and relations, Plato does Calvo and Luc Brisson, eds., Interpreting the not: instances of humanity and triangularity Timaeus‑ Critias: Proceedings of the IV Sympo‑ are just as ‘insubstantial’ as instances of white sium Platonicum : Selected Papers. Academia Verlag. 179‑186. ness and heat. I have not, however, put forth Fine, Gail. 1983. “Relational Entities.” Archiv für Ge‑ the stronger thesis here that particulars are schichte der Philosophie 65: 3. 225 – 249. only composed of tropes, i.e., that they are … 1986. “Immanence.” Oxford Studies in Ancient Phi‑ bundles of tropes, since I have not directly losophy 4. 71 – 97. addressed the status of the sole member of Gill, Mary Louise. 1987. “Matter and Flux in Plato’s the third ontological category, the Receptacle. Timaeus.” Phronesis 32: 1. 34 – 53. Given, however, that particulars can success Gilmore, Cody. 2013. “Slots in Universals.” Oxford Studies in Metaphysics 8. 187 – 233. fully be resolved into tropes, there seems little Gregory, Andrew. 2000. Plato’s Philosophy of Science. philosophical reason to take the Receptacle to Duckworth. be a substratum in which those tropes inhere. Harte, Verity. 2010. “The Receptacle and the Primary It is more parsimonious to take particulars as Bodies: Something from Nothing?” In Mohr bundles of co‑located tropes in the space of and Sattler, eds., One Book, One Universe. 131 the Receptacle. Even if we do not fully accept – 140. such a bundle theory, however, the ontology of … 2002. Plato on Parts and Wholes: The Metaphysics of Structure. Clarendon. particulars in the Timaeus is not a substance Johansen, Thomas Kjeller. 2004. Plato’s Natural Phi‑ 31 ontology but a trope ontology. losophy. Cambridge. Lee, Edward. 1967. “On Plato’s Timaeus, 49D4 ‑E7.” The American Journal of Philology 88: 1. 1 – 28. 22 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
… 1966. “On the Metaphysics of the Image in Plato’s … 2000. Plato: Timaeus. Hackett. Timaeus.” The Monist 50. 341 – 368. … 1975. “Plato and Talk of a World in Flux: Timaeus Lewis, David. 1986. “Against structural Universals.” 49a6‑50b5.” Harvard Studies in Classical Philol‑ Australasian Journal of Philosophy 64:1. 25 – ogy 79. 125–148. 46. Lowe, E. J. 2006. The Four‑Category Ontology: A Meta‑ physical Foundation for the Natural Sciences. Oxford. NOTES McCabe, Mary Margaret. 1994. Plato’s Individuals. Princeton. 1 Ferber 1997 also addresses the question of why there are Forms in the Timaeus, giving an analysis of the McPherran, Mark. 1988. “Plato’s Particulars.” The brief argument for Forms at 51d3‑52a7. See his 182‑4, Southern Journal of Philosophy 26: 4. 527 – for an alternate account of particulars in the Timaeus as 553. relational entities rather than substances. Mertz, Donald. 1996. Moderate Realism and its Logic. 2 There are many accounts of tropes, and I Yale. cannot here give a detailed comparison between Plato’s tropes and contemporary trope s— this is work for Miller, Dana. 2003. The Third Kind in Plato’s Timaeus. another paper. There is some similarity, however, between Vadenhoeck & Ruprecht. Plato’s trope ontology and Lowe’s four‑category ontology Mohr, Richard D. 2005. God and Forms in Plato. Par — one dissimilarity is that Plato’s ontology contains only menides Publishing. three categories, Forms (transcendent universals), tropes, and the Receptacle (substantival space). For a defense … 1985. The Platonic Cosmology. Brill. of taking the Receptacle to be substantival space, see … 1980. “Image, Space, and Flux in Plato’s Timaeus”. Buckels 2016a. For contemporary accounts of tropes, see, Phoenix 34: 2. 138 – 152. e.g., Ehring 2011, Lowe 2006, Campbell 1990, Armstrong 1989, and Williams 1953. Mohr, Richard D. and Barbara M. Sattler. 2010. One 3 All textual references are to Burnet’s OCT Book, The Whole Universe: Plato’s Timaeus To‑ Timaeus and translations are my own, unless otherwise day. Parmenides Publishing. indicated. Note that Plato uses “τοιοῦτον” in many dif Nehamas, Alexander. 1973. “Predication and Forms of ferent ways in the dialogues; I am not claiming that every Opposites in the ‘Phaedo’.” The Review of Meta‑ use of “τοιοῦτον” is a reference to something that comes physics 26: 3. 461 – 491. to be, only that Plato uses it thus in key passages of the Timaeus. Prior, William J. 1985. Unity and Development in Plato’s 4 Miller 2003, 82, argues that the proscription Metaphysics. Croom Helm. generalizes only to ‘all the elements,’ not “everything that Schaffer, Jonathan. 2001. “The Individuation of comes to be.” This coheres with his reading of the entire Tropes.” Australasian Journal of Philosophy passage as restricted to elements. Harte 2002, 252, n. 162, 79: 2. 247 – 257. similarly doubts that the proscription generalizes to all things, since the initial problem “is closely tied to the role Silverman, Allan. 2002. The Dialectic of Essence. Prin of earth, air, fire, and water, as candidate elements in the ceton. traditional sense.” Broadie 2012, 202‑3, also agrees. On … 1992. “Timaean Particulars.” The Classical Quarterly this, Miller 2003, 81, writes that “Plato is not concerned 42: 1. 87 – 113. with ‘phenomenal fire’ but with the element fire that we observe,” distinguishing between the two so as to avoid White, F. C. 1981. Plato’s Theory of Particulars. Arno the generalization from phenomenal fire to phenomena Press. in general. But it is difficult to distinguish elemental and Williams, D. C. 1953. “On the Elements of Being: I.” phenomenal fire, since, as Miller admits, we observe The Review of Metaphysics, 7(1): 3–18. elemental fire, at least when aggregated: it is visible and, in fact, part of all visible things (31b5), so it seems likely Zeyl, Donald J. 2014. “Plato’s Timaeus.” The Stanford that Timaeus generalizes his argument regarding fire— Encyclopedia of Philosophy (Spring 2014 Edi the visible element—to all visible particulars, which all tion), Edward N. Zalta (ed.), URL =
the elements to all sensible phenomena is legitimate always in fact points to the permanent, unchanging, and (even if he in fact extends it), since the initial puzzle is characterless receptacle in which are constantly occur only about the changing of one element into another. ring transient and indeterminate manifestations of the But the elements are the basis for all other sensible determinate characteristics just mentioned [‘the such and phenomena, so if the elements are so unstable that they such, whatever the correct formula may be, that is always might transform into each other at any moment, then the identical in each and all of its occurrences’].” things composed of the elements seem to be vulnerable 11 Zeyl 2000, lviii‑lix; cf. Silverman 2002, 258‑60. to the same change. Indeed, Timaeus only holds that it 12 Cf. Silverman 2002, 260: “What is at stake is possible for one element to cease to be and another to between the reconstructionist [alternative interpretation] take its place at any time, and it seems true that any given and the tradition is not so much these linguistic formulae physical object x may cease to be what it is at any instant [i.e., how to address particulars] but rather the account of and be replaced by a non‑identical, even if extremely the phenomena themselves.” similar, y. 13 Zeyl 2000, lxi. Cf. Mertz, 83f, on Plato’s “con 5 Timaeus ‘restarts’ his cosmogony after about crete individuals.” twenty Stephanus pages, so there is a ‘first’ and a ‘second’ 14 Cf. Cornford 1937, 28‑32, Prior 1985, 95. account of the creation of the universe. I take it that the 15 Mohr 1985, 108‑15, also argues for such a view. two accounts are largely compatible, with the second For discussion of how the triangles come together to form building upon the first (for one thing, the Receptacle is bodies, see, e.g., Cornford 1937, 210‑30. added in the second, so we have a tripartite, rather than 16 Silverman 2002, 282, writes that there is an a dualistic, ontology), but this is not uncontroversial. “inexplicable coincidence of geometrical bodies oc Broadie 2012, 201‑2, Johansen 2004, 117, Silverman 2002, cupying space and properties entering and exiting the 248‑56, and Harte 2002, 213‑226, also seem to take the place defined by those bodies.” He thinks that there is two accounts as complementary, although, e.g., Silverman no essential connection between a certain arrangement sees the first account as giving us “traditional forms” of geometrical form‑copies (my Form images) and a while the second gives us “geometrical forms,” and he certain grouping of “traditional” form‑copies (hot, yel then joins these such that geometrical forms ground mat low, fire, etc.). Thus is it a coincidence that quantitative ter and place while traditional forms ground qualities. and qualitative form‑copies always fit together, with the 6 Cf. Broadie 2012, Ch 3, esp. 70‑74, who argues qualities entering and exiting the place of the quanti that the “Intelligible Animal” here (my “Living Being”) is ties. But I think Silverman (esp. 249f) makes too much not a “thick intelligible,” although she admits her argu of distinguishing geometrical from traditional Forms; ment is not decisive. I argue that an image of Triangularity is just another 7 It is worth pointing out that Form images be τὸ τοιοῦτον. Thus, on my account, Fieriness is a certain ing τὰ τοιαῦτα, and τὰ τοιαῦτα being tropes, is compat species of Tetrahedral Pyramid. Harte 2002, 262‑3 and n. ible with either of the two major interpretations of the 189, has a position similar to mine: “particles of earth, air, Receptacle, namely, that it is a substratum (in which case fire, and water, as constructed by the demiurge, imitate tropes would inhere in it) and that it is space (in which forms through their geometrical construction; they are case tropes would be located in its regions). See also note structures of space, whose properties, perceptible and 30. other, are parasitic upon their geometrical structure.” 8 Silverman 2002, passim, also recognizes the Harte avoids Silverman’s problem (the ‘inexplicable coin importance of Form images, which he calls Form copies. cidence’ of geometrical Forms) but does not explain how His Form copies differ from my Form images in several geometrical constructions imitate elemental Forms, since ways, some of which have to do with our readings of the she stops short of identifying Fire with a geometrical Phaedo. With respect to the Timaeus, the biggest differ structure: Harte does not suggest “that the forms of fire ences between our readings (which are both indebted to and earth are themselves [the type] regular solids.” Cherniss 1954 & 1957) lie in our treatment of the Recep 17 Cornford 1937, 190, denies that Fire is a tacle (see Buckels 2016a) and geometrical versus “traditio certain structure, because we do not say, when we see fire, nal” Forms (see notes 15 & 19). More broadly, Silverman “there are some pyramids.” Instead, Fire is a combina argues that Form copies cannot be destroyed, whereas my tion of certain qualities. The Form is the “meaning of the Form images come to be and perish; Silverman’s Form name ‘Fire,’” and the “quality is the copy” of the Form.
copies are thus difficult to distinguish from Forms. While But we do not deny that water is H2O — even that it is
Silverman and I both argue that sensible particulars (i.e., essentially H2O — even though we do not, before our
physical objects) are entirely composed of Form copies (in first chemistry lesson, say, “there is some H2O.” “Water” my case, Form images), Silverman retains particulars as refers to a combination of certain qualities, but this does
a distinct category of Plato’s ontology, while I think they not prevent us from saying that it is essentially H2O. Cf. reduce entirely to Form images (see note 29). White 1981, 331‑4. 9 Cf. Silverman 2002, 261‑5, and Zeyl 2014, §6 18 Cf. Lewis 1986 for discussion of structural 10 Cf. Cherniss 1954, 128: “If at any time universals and Gilmore 2013 for slots in universals. anywhere one tries to distinguish any phase of the 19 Cornford 1937, 198‑206, instead argues that phenomenal flux from any other by saying “this,” one the nature of fire is qualitative. For criticism of Cornford, 24 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory
see Mohr 1985, 108‑15. Johansen 2004, 126‑7, seems to ‑such’ comes around in similar fashion each time: there give a qualitative explanation, too. need not be the same this‑such each time, as the imma 20 Silverman 2002, 278‑81, holds that matter nent universalist would have it, but a this‑such need only or corporeality is an emergent property, a result of the come to be ‘similarly’ each time the appropriate circum arrangement of geometrical form‑copies. If by this he stances arise. Even if we do take ὅμοιον with τὸ τοιοῦτον, means that corporeality, the property of being a body, however, tropes are salvageable, since we have an account is instantiated whenever triangular form‑copies are of what it is for two tropes to be similar, namely that they arranged to form a solid, then this seems right. Cf. Silver are images of the same Form. man 2002, 255f, and Cornford 1937, 181. 29 Cf. Rep. 476b4‑6, where things are said, in 21 The position I have in mind here is that the Re passing, to be made out of sounds and colors and figures ceptacle acts as a kind of matter or stuff that is contained (τάς τε καλὰς φωνὰς ἀσπάζονται καὶ χρόας καὶ σχήματα by the geometrical shapes rather than the view that there καὶ πάντα τὰ ἐκ τῶν τοιούτων δημιουργούμενα). While is some primitive matter in the Receptacle (and distinct I merely explain and defend a Platonic trope theory here, from it), as found, e.g., in Gill 1971; cf. McCabe 1994, 180. in an unpublished manuscript I explore and defend a I find this latter suggestion implausible, too, as well as Platonic trope bundle theory. unmotivated by the text; for fairly definitive criticism of 30 It is worthwhile to point out that, if the mem Gill’s view, see Silverman 2002, 267‑73. bers of the class of Becoming are tropes, then the motiva 22 As an aside, holding that triangles compose tion for taking the Receptacle to be a substratum has been the universe hardly seems weirder than holding that the dealt a serious blow. Substances—particulars that are strings of string theory, or any other posit of speculative supposed to be composed of tropes and a substratum— physics, compose the universe! feature nowhere in Plato’s tripartite ontology if not in 23 Gregory 2000, 203‑5, argues that the elemental the category of Becoming. But they cannot be in this triangles undergo no intrinsic change—the only triangles category, since one of their components—tropes—makes that can change are the triangular faces of the elements up this category, and another of their components—the air, fire, and water. It is the faces, then, that are “new or Receptacle, taken as a substratum—makes up a different “old,” not the elemental triangles. category. Thus substances would have to be a conglom 24 E.g., Schaffer 2001, 247, although Schaffer eration of the two categories, Form‑images and the argues that tropes are better described as “here‑suches.” Receptacle, whereas, in the text, Form‑images are said to Cf. Ehring 2012, 76‑91. be the product or ‘offspring’ of Forms and the Receptacle 25 By universals, I mean that Forms are tran (50d2‑4). There is plenty of room for particulars in Plato’s scendent universals, i.e., non‑spatiotemporal entities that ontology, but only if they are wholly composed of tropes, explain the common features of particulars without being as I argue in Buckels 2016a. The argument of this paper, “in” or located with those particulars. The traditional together with the argument of that paper, go most of the relation of “participation” is replaced with a Form image way toward establishing Plato as a trope‑bundle theorist. “being an image of” a Form, which we may interpret as 31 I would like to thank Thomas Chance, Cody the relation between a trope and its transcendent uni Gilmore, Peter Larsen, John Malcolm, Vasilis Politis, versal. The transcendent universal explains resemblance Allan Silverman, and Jan Szaif for valuable discussion of among tropes, as each trope is an image (instance) of a this paper and previous drafts, as well as audiences at the Form (universal). Plato does not clearly commit himself Eastern and Central Division Meetings of the American to a range of Forms; here I assume a Form for every Philosophical Association, the London Ancient Science meaningful predicate, but I examine this assumption Conference, the University of California Davis, and Trin further in an unpublished manuscript. ity College Dublin. 26 See, e.g., Fine 1983 & 1986 for the view that Forms are immanent in particulars. 27 Cf. Mohr 2005, 87: “We can tell that what recurs is the same recurring image by referring it to the original of which it is an image.” 28 Cf. Ferber 1997 about the justification of Forms here. The point about the same Form being im aged in each ‘this‑such’ is strengthened if we take ὅμοιον in 49e4‑7 (the “similar fashion” in “this‑such coming around always in similar fashion in each case and all together”) as modifying the “coming around” with Miller 2003, 81, rather than as modifying τὸ τοιοῦτον (49e5). If we take it with τὸ τοιοῦτον, we might be inclined toward the immanent universal interpretation; the resulting translation, following Zeyl 2000, would read: “‘what is such,’ coming around like it was, again and again.” But if we take it adverbially with περιφερόμενον, then ‘this